3x(x-2)+5=2(5x-4)

Solution for 3x(x-2)+5=2(5x-4) equation:

3x(x-2)+5=2(5x-4)

We move all terms to the left:

3x(x-2)+5-(2(5x-4))=0

We multiply parentheses

3x^2-6x-(2(5x-4))+5=0


We calculate terms in parentheses: -(2(5x-4)), so:

2(5x-4)

We multiply parentheses

10x-8

Back to the equation:

-(10x-8)


We get rid of parentheses

3x^2-6x-10x+8+5=0

We add all the numbers together, and all the variables

3x^2-16x+13=0

a = 3; b = -16; c = +13;
Δ = b2-4ac
Δ = -162-4·3·13
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10}{2*3}=\frac{26}{6}
=4+1/3
$